What is the rate of change and initial value for the linear relation that includes the points shown in the table?
x y
1 10
2 8
3 6
4 4
initial value: 12, rate of change: −2
initial value: 8, rate of change: 2
initial value: 12, rate of change: 2
initial value 8, rate of change: −2

Let us first find the slope, or rate of change, denoted by m in the linear equation y=mx+b

m=(y2-y1)/(x2-x1), in this case

m=(8-10)/(2-1)

m=-2/1

m=-2  (since this is a line it is constant and we don't have to check other points so see if the slope changes :P)  now we have:

y=-2x+b, we can use any point now to solve for b, the y-intercept (y-intercept is the value of y when x=0), I'll use point (1,10)...

10=-2(1)+b

10=-2+b

12=b so our line is:

y=-2x+12  (note that the y-intercept, b, is the initial value)

So.

Initial Value: 12, rate of change: -2